THE FIRST ANSWER GETS A BRAINLIEST BUT THE ANSWER HAS TO BE RIGHT ALSO 20 POINTS Kiah plotted the locations of her home and the city of Huntingdon on the number line shown. Williamsburg is the same distance from Kiah’s home as Huntingdon, but it is in the opposite direction. Which statement best describes how to find the location of Williamsburg on the number line?
A) The opposite of 6.75 is −6.75, so Williamsburg is at −6.75.
B) The sum of 6.75 and 6.75 is 13.5, so Williamsburg is at 13.5.
C) The numbers 6.75 and −6.75 are the same, so Williamsburg is at 6.75.
D) Opposites, such as 6.75 and −6.75, sum to zero, so Williamsburg is at 0.

Answer:

• 7%: $1065
• 13%: $1365

Step-by-step explanation:

If x represents the amount invested at 7%, then the amount invested at 13% is x+300. Lydia's total interest is ...

  0.07x +0.13(x +300) = 252

  0.20x = 213 . . . . . subtract 39

  x = 213/0.20 = 1065

Lydia has $1065 invested at 7% and $1365 invested at 13%.

Final answer:

Using the given conditions, we set up and solve an equation where x is the amount invested at a 7% rate and x + $300 is the amount at a 13% rate. After solving, we find that Lydia has $1065 in the 7% account and $1365 in the 13% account.

Explanation:

Let's assume Lydia's investment at 7% to be x and her investment at 13% to be x + $300. Since the total interest is $252, we can create an equation to solve for the values of x.

The equation will look like this:

0.07x + 0.13(x + 300) = 252

Let's solve the equation:

0.07x + 0.13x + 39 = 252

Combine like terms to get 0.2x + 39 = 252

Subtract 39 from both sides to get 0.2x = 213

Divide by 0.2 to solve for x, which gives x = 1065.

So, Lydia has $1065 in the 7% account and $1065 + $300 = $1365 in the 13% account.

Learn more about Investment here:

brainly.com/question/34489138

#SPJ3

Answer:

Explained below.

Step-by-step explanation:

When drawing line of symmetry on a figure and reflecting, we have to know that pairs of segments in that figure must have the same length while pairs of angles must have the same measurement. This is to ensure that half of that figure must concise with the other half part of it when that figure is folded across a line of symmetry.

Final answer:

The roots of the polynomial function f(x)=(x-3)*(x+6)² are 3 and -6.

Explanation:

The polynomial function f(x)=(x-3)*(x+6)² can be factorized as follows:

f(x) = (x-3)*(x+6)*(x+6)

This means that the expression (x-3) represents one of the linear factors of the polynomial, while (x+6) represents a quadratic factor. To find the roots of the polynomial, we set each factor equal to zero and solve for x:

(x-3) = 0 -> x = 3

(x+6) = 0 -> x = -6

Therefore, the roots of the polynomial function f(x)=(x-3)*(x+6)² are 3 and -6.

Learn more about Polynomial roots here:

brainly.com/question/31214281

There are 95 cards did Steve initially purchase to begin his collection.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Steve began a baseball card collection by purchasing some cards.

And, He increased the number of cards in the collection by a constant amount each week after that.

Now, In 3 weeks he collect 285 cards.

Hence, Number of cards to collect in initially is,

⇒ 285/3

⇒ 95

Thus, There are 95 cards did Steve initially purchase to begin his collection.

Learn more about the divide visit:

brainly.com/question/28119824

#SPJ6

Answer:95

Step-by-step explanation:

95x3=285

Answer:

wire for square to maximize total area = 23 m

Wire to minimize total area = 2.019 m

Step-by-step explanation:

For the square, let's say the total length of the square is "y" m.

Thus, length of one side is = y/4

And area of the square = (y/4) = y²/16

Since the wire is 23 m, then total length of equilateral triangle is; 23 - y.

Thus, length of one side of equilateral triangle = (23 - y)/3

Using trigonometric ratio, we can find the height of the triangle and thus area.

Area of triangle = (√3)/4) × ((23 - y)/3)²

Area of triangle = (√3)/36)(23 - y)²

So, total area of square and triangle is;

A_total = (y²/16) + (√3)/36)(23 - y)²

Now, extremizing this function by derivatives, we have;

dA/dy = (y/8) - (√3)/18)(23 - y)

d²A/dy² = ⅛ + (√3)/18)

So, d²A/dy² > 0

Now,let's find the maximum or minimum of the function.

So, we equate dA/dy to zero.

Thus;

(y/8) - (√3)/18)(23 - y) = 0

y/8 = (√3)/18)(23 - y)

(y/8) + (√3)/18)y = 23((√3)/18)

Multiply through by 8 to give;

y + 0.0962y = 2.2132

1.0962y = 2.2132

y = 2.2132/1.0962

y = 2.019 m

2.019 will be a minimum because d²A/dy² > 0

The maximum will occur at a boundary of the allowed values. Thus, the absolute maximum is for y = 23.

Note that a square has more area than a triangle and as such it is normal for the square to get the largest area over the triangle and therefore we will have to use all of the wire to construct the square.